New York Governor Andrew Cuomo speaks outside New York City Hall in September.

New York Gov. Andrew Cuomo’s favorability rating has spiked to its highest level in nearly a year, while New Jersey Gov. Chris Christie’s has fallen to its lowest ever among New York state voters, according to a poll to be published Monday by Siena College.

Mr. Cuomo, a Democrat facing re-election this year, is viewed favorably by 66% of voters, the poll found, an uptick from his 61% rating in November and his highest rating since February 2013. And his job-performance rating jumped by 10 points, to 54%, since November.

Mr. Christie, a Republican whose administration is engulfed by a scandal involving the closure of lanes to the George Washington Bridge as alleged political retribution, lost standing with New York voters, as his favorability rating fell by 14 points to 49%, from 63% in November.

The poll also found that Mr. Cuomo would trounce potential Republican gubernatorial opponents in this year’s race, including Westchester County Executive Rob Astorino, whom he would beat by 67% to 19%. In a hypothetical match-up with Donald Trump, one of the only other names to be floated as a Republican contender, Mr. Cuomo would win by 70% to 22%.

The governor, who delivered his state of the state address earlier this month, saw solid voter approval for a broad range of the policy priorities he outlined, including key pieces of his tax-cut plan such as enacting a property-tax circuit-breaker and lowering the top rate on the estate tax (both received 77% approval).

Support for a system of public financing for political campaigns, which Mr. Cuomo failed to advance in Albany last year but has pledged to back again this year, received its highest-ever approval, at 64%.

Voters expressed mixed reactions, however, to potential medical marijuana legalization. While 49% of voters support legalizing the drug for medicinal purposes, only 28% support the governor’s pilot program, which would allow 20 hospitals statewide to prescribe marijuana for patients with diseases such as cancer or glaucoma.

The poll, conducted Jan. 12-16, surveyed 808 New York State registered voters, with a margin of error of 3.4 percentage points.